Method for controlling a wind-up, including determining running parameters based on models taking un-winding into account

ABSTRACT

A wind-up is controlled by preparing a winding recipe ( 13 ) of a roll, which winding recipe comprises winding parameters. Based on calculatory and/or experimental models, running parameters of the wind-up are determined before the run such that, based on the models, the roll will withstand unwinding taking place in an end-use device without being damaged.

CROSS REFERENCES TO RELATED APPLICATIONS

This application is a U.S. national stage application of InternationalApp. No. PCT/FI2003/000851, filed Nov. 10, 2003, and claims priority onFinnish App. No. 20022023, Filed Nov. 13, 2002, the disclosure of whichis incorporated by reference herein.

STATEMENT AS TO RIGHTS TO INVENTIONS MADE UNDER FEDERALLY SPONSOREDRESEARCH AND DEVELOPMENT

Not applicable.

BACKGROUND OF THE INVENTION

When, in wind-ups known from prior art, the wind-ups of newslitter-winders are started up or the winding of new paper grades isstarted using slitter-winders already in use, the structure of the rollis controlled by so-called winding parameters, nip load, the tension ofthe web before the wind-up, and winding force, which, in knownapplications, are set, based on experience, as a function of thediameter of the roll to be so-called winding recipes. The initialguesses for the winding recipes generally originate from otherslitter-winders, with which the same or a similar paper grade has beenrun. However, due to the great variation in the properties of papergrades having the same grade name when run in different paper machines,case-specific trial runs are always necessary in order to determine thewinding recipe. Each paper grade and end diameter of a roll is usuallyprovided with a winding recipe of its own.

In applications known from prior art the quality of the finished rollscoming from the wind-ups is primarily determined based on visualestimation. In most slitter-winders the rolls also undergo occasionalmeasurements; most often the hardness of the roll is measured by meansof a manually operated roll hardness sensor.

It is also known from prior art to provide the slitter-winders withsurface density calculation and display. In these known applications thesurface density value corresponding to an arbitrary roll diameter hasbeen determined from the surface of the roll based on the change in thethickness of the paper.

Applications are known from prior art in which the object is to estimatethe stresses within the roll with the help of measurements. Patentapplication WO 9950719 “Verfahren und Anordnung zur neuronalenModellierung einer Papierwickel Vorrichtung” discloses a method in whichthe tension of the web when it goes into a roll is determined by meansof learning via neural networks. This enables the calculation, with thehelp of winding models, of a two-dimensional stress distribution insidethe roll. Patent application DE 19821318 “Verfahren zum Überwachen derWickerhärte einer Wickelrolle” discloses a method for the measurement ofthe tension of the web when it goes into a roll, which method is basedon measuring the change in the web length on the basis of colored marksprinted on the web.

A large number of the winding defects generated during winding will gounnoticed when visual estimation or measurement with a hardness sensoris used, David R. Roisum: “How to Measure Roll Quality”, Tappi Journal71(10) 1988, David R. Roisum: “Reading a roll”, Tappi Journal 81(4)1998. Even if the two-dimensional stress distribution of the rolls couldbe calculated using the procedure of the patent applications WO 9950719and DE 19821318, in most cases it would not be possible to prevent thegeneration of potential or actual winding damage, because the abovemethods do not take into account the causes of damage due to the loadsdirected to the roll in a paper mill slitter-winder (winder) and in thepaper mill customer's finishing device.

For the paper manufacturer, however, the most important and criticalfeedback on the quality of the rolls comes from the customers, such asprinting houses, for example in a case where running problems haveoccurred when the rolls have been run, for example, in a printingmachine. In such a case the corrective measures in the papermanufacturing process or in the winding recipes of the slitter-windercan only be taken after a delay of several days or even weeks. If thefrequency of the variations in the properties of paper (mass, surfaceproperties) is greater, there is no sense in taking corrective measures.

Due to the above-mentioned quality feedback delay, when starting up newslitter-winders or when starting the winding of new paper grades usingslitter-winders already in use, the search for winding recipes is oftenslow.

A particular problem in the selection of the winding parameters of thewinding recipes is that most defects cannot be noticed on the basis ofvisual examination and are not always discovered through surface densityor equivalent measurements, and, as explained above, getting actualfeedback on quality takes long.

SUMMARY OF THE INVENTION

An object of the invention is to provide a method by means of which thewinding parameters can be determined so as to make sure that the rollwithstands handling both in the paper mill and at the customer end.

Another object of the invention is to provide a method by means of whichthe problems described above are eliminated or at least minimized.

A special object of the invention is to provide a control method forcontrolling a wind-up, which method also takes into account the loadsdirected to the roll in the wind-up and in the paper mill customer'smachinery.

An essential advantage of the invention is that it is based on the ideaof providing a roll which will go through its entire life span withoutbeing damaged, whereas models and systems known from prior art aim toprovide, on the wind-up, an optimal roll with respect to winding.

In the method according to the invention for controlling a wind-up, inwhich method a winding recipe is prepared containing winding parameters,running parameters of the wind-up are determined on the basis ofcalculatory and/or experimental models before the run such that, basedon the models, the roll will withstand the winding up taking place inthe end-use device without being damaged. According to an advantageousadditional feature in the method according to the invention the runningparameters of the winder are determined such that, based on the models,the roll will withstand the winding up taking place in the wind-up.According to a further advantageous additional feature in the methodaccording to the invention the winding recipe of the roll is formed as afunction of the diameter or radius or the degree of thickness of thecumulated paper on the winding core or as a function of wound web lengthor the number of laps of the wound web.

According to an advantageous application of the invention the internalstress distribution of the rolls is measured, the forces directed to theroll during winding are calculated by means of a load model and therelaxation of the internal stresses of the roll during transportation isestimated by means of the model and the forces directed to the roll inthe paper mill customer's finishing devices are calculated by means ofthe load model.

According to an advantageous application of the method according to theinvention:

-   a) the internal stress distribution of the roll being wound up is    measured indirectly in three or two dimensions-   b) the internal stresses caused by forces directed to the roll    during winding are calculated with the help of a roll load model,    Kilwa Ärölä: “A Simulation Program for Hyperelastic Rolling Contact    Model”, Master of Science Thesis, Helsinki University of Technology    2001.-   c) the relaxation of the internal stresses of the finished roll,    before the roll is processed in the paper mill customer's finishing    device (e.g. a printing machine), is estimated and-   d) the stresses and displacements directed to the roll during    unwinding are calculated by means of a load model (RAMA) of the roll    and the unwinding device.

The information on the paper material needed in the method according tothe invention is partially obtained through off- and on-linemeasurements of the paper processing equipment preceding theslitter-winder and partially through measurements of the slitter-winderitself (e.g. radial and tangential modulus of elasticity).

In the method according to the invention the winding recipe is,according to an advantageous application, sought such that the stressdistribution of the roll, calculated with the WOT model(WOT=Wound-On-Tension i.e. the tension of the uppermost layer on the webroll, sometimes also referred to as WIT=Wound-In-Tension), M. Jorkama:“Contact Mechanical Model for Winding Nip”. Dissertation, HelsinkiUniversity of Technology, 2001, the roll structure model and the rollrelaxation model provides damage-free unwinding on the finishing deviceaccording to the RAMA model (=load model of the end-use device). In thesearch for the winding recipe, account has to be taken of the physicalproperties of the winding device and of ensuring damage-free winding andrunnability on the slitter-winder, which are estimated with the loadmodel of the wind-up. During running of the slitter-winder the recipe isbeing fed back on the basis of WOT measurement so that a stressdistribution according to the previous step is generated in the roll.

In the roll structure measuring method it is possible to use a WOTestimated through the change in the web length measured, for example, bymeans of laser speed sensors. The structure of the roll is in such acase calculated using the Hakiel model, Z. Hakiel: “Nonlinear Model forWound Roll Stress”. Tappi Journal 70(5) 1987, or an equivalent model,Zabaras N., Liu S., Koppuzha J. and Donaldson E. “A Hypoelastic Modelfor Computing the Stresses in Center-Wound Rolls of Magnetic Tape”Journal of Applied Mechanics, Vol 61 No. 2, pp. 290-295, 1994. It isalso possible to make use of a method utilizing the density of the roll,paper thickness and the winding model, David R. Roisum: “The Measurementof Web Stresses During Roll Winding“. Dissertation WHRC at OSU 1990.

In the structure models of the slitter-winder wind-up and the finishingdevice, slippages generated within the roll and possibly other damagemechanisms as well are calculated. With the help of the calculatedslippages the damage potential of the roll is estimated by usingempirical data and roll damage models, N. Vaidyanathan and J. K. Good:“The Importance of Torque Capacity in Predicting Crepe Wrinkles andStarring within Wound Rolls”. Proceedings of the 3^(rd) IWEB conference.OSU 1995, Lee, Ban-Eop: “Buckling Analysis of Starred Roll Defects inCenter Wound Rolls”. Dissertation WHRC at OSU 1991.

When estimating the relaxation of the stresses of the finished roll,known viscoelastic winding models are used, such as the reference: W. R.Qualls and J. K. Good: “A Nonlinear Orthotropic Viscoelastic WindingModel”. Proceedings of the 3^(rd) IWEB conference. OSU 1995.

The method according to the invention renders winding “intelligent” i.e.the feedback between the quality of the roll and the winding parameters,which before had taken several days or weeks, can now be carried outduring the running of the slitter-winder. Reactions to changes in thepaper properties and in the production conditions in the paper mill takeplace automatically and immediately.

By means of the method according to the invention it is possible todetermine quickly the optimal winding recipes, when starting up newslitter-winders or when starting the winding of new paper grades usingslitter-winders already in use.

The method according to the invention enables optimal individual controlof the winding stations, which also reduces variations in qualitybetween the rolls of the same set.

By way of summary, in the method according to the invention, thecontrolling of the wind-up is based on a prediction drafted with thehelp of a model on the runnability of the roll in end-use, in whichprediction, according to an advantageous application, a WOT vs. diameterreference curve providing optimal runnability during end-use in thefinishing device is determined by iterating the model before the run.According to advantageous characteristics of the invention, the runningparameters of the wind-up of the slitter-winder are adjusted such thatthe measured WOT curve corresponds to the WOT reference curve obtainedby iterating the model. The WOT reference curve may also be modifiedbased on the runnability prediction provided by means of the windingmodel. When making the runnability prediction, the roll stressrelaxation model is advantageously made use of and the initial estimatefor the running parameters is most appropriately calculated using thewinding nip model.

The invention will now be described in more detail with reference to thefigures of the accompanying drawing, to the details of which theinvention is, however, by no means intended to be narrowly confined.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 schematically shows the basic principle of the method accordingto the invention.

FIG. 2 schematically shows by means of an example a WOT curve selectionprocedure used in the method according to the invention.

FIG. 3 schematically shows an example in the method according to theinvention for establishing an initial value of a winding recipe.

FIG. 4 schematically shows a subprocess of FIG. 1 during the running ofa slitter-winder, the slitter-winder having WOT measurement.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 1 shows the basic principle of an application of the methodaccording to the invention. The starting data 11 needed includes basicinformation on the paper to be wound, such as thickness, frictioncoefficient, elastic moduli in thickness and machine direction,information on the viscoelastic properties of the paper, airpermeability and surface roughness, etc., mechanical data on the wind-updevice as well as mechanical data on the end-use device of the roll oron the unwinding device on which the unwinding will take place. In stepI an appropriate WOT curve 12 is selected. This selection process willbe explained in more detail in the description of FIG. 2. To enable theutilization of this WOT curve WOT_(ref)(D) (D=roll diameter) the wind-upmust incorporate a method for calculatory or measurement-basedestimation of WOT. In the subsequent step II a winding recipe 13R_(ref)(D) is selected that produces, according to the winding model ofthe slitter-winder, step III 14, a WOT curve 12 WOT_(ref)(D) accordingto step I. After this, in step IV, the load model of the winding deviceis used to check further that the rolls to be wound up withstand theloads 15 produced in the winding process. If the winding model indicatesthat the rolls withstand the loads, the process can be continued, i.e. atransition to step V is made, otherwise a new recipe is generated, i.e.there is a return to step II R_(ref)(D), which new recipe provides,based on calculation, the selected WOT curve 12 WOT_(ref)(D), and stepsIII and IV are gone through again. If, after this, there is still needto continue iteration, a new recipe can be generated, for example, bymeans of a so-called secant method, Erwin Kreyszig: “AdvancedEngineering Mathematics”. Sixth Edition, John Wiley & Sons, Inc. 1988,p. 956, meaning that a gradient approximation in the winding parameterspace is formed of the recipes of two successive iterations, the maximumstresses of the roll, for example, being the object function to beminimized. A limiting condition for the minimization task is that thewinding recipe produces, in step I, a WOT curve 12 selected on the basisof calculation. Let us assume, for the sake of simplicity, that awinding recipe is established by iteration as described above which,based on calculation, a) withstands the winding process and b) gives theselected WOT curve. Were such a recipe not found, it would be necessaryto return to step I and establish a new WOT curve WOT_(ref)(D), etc. Asstated, it is assumed here that an appropriate recipe has been found andthe operation of the slitter-winder 16 can be started, i.e. a transitionto step V can be made. If no WOT measurement has been performed in thewind-up or slitter-winder, the slitter-winder is run in step V with therecipe R_(ref) 13 without changing the recipe during the running. If thewind-up or slitter-winder has WOT measurement, the procedure is asfollows: During the run this recipe R_(ref) selected in the precedingstep is corrected so as to provide the WOT curve 12 WOT_(ref)(D)according to step I. The correction of the recipe 13 is made, forexample, by adjusting primarily winding force, secondarily nip load, andfinally tension. Increasing each winding parameter increases WOT. Theadjustment can be carried out, for example, as a simple PID controller,K. Åström & T Hägglund: “PID Controllers: Theory, Design, and Tuning”.2nd edition, 1995, pp. 59-119. If, in the next run, the paper grade andstarting data remain substantially the same, the realized winding recipe17 according to step VI can be adopted directly as the winding recipe 13of step II of the next run. The basic principle has been illustratedabove by way of a simple example only. Further adjustments andmeasurements may be added to this basic frame. For example, after stepIV it is possible to calculate, by means of the realized winding recipe17, the winding model of the slitter-winder to detect possible windingdefects. The end result is checked before the next run. If thecalculation showed that the rolls withstand the load, no furthermeasures are needed. If, however, the calculation suggested a highprobability of damage, iteration of an appropriate WOT curve 12 has tobe started or additional limitations for the winding parameters have tobe set.

FIG. 2 describes the selection procedure of the WOT curve 12 in moredetail by means of an example. The basic principle for the selection ofthe WOT curve 12 is that, based on some argument, said WOT curve 12provides damage-free unwinding in the end-use device of the roll. Theargument used can be, for example, the calculation model RAMA 23, stepIIc, as in this example, or a statistical model or data or a combinationof these. The procedure begins with selecting, in step I, an initialguess as the WOT curve WOT₀(D), i.e. initialization of iteration iscarried out 22 WOT_(i)=WOT₀ (D), where D=roll diameter. This may be, forexample, a constant independent of the diameter, where the value of theconstant may be 15-20 percent of the tensile strength of the web. Afterthis, in step II, step IIa, the stress distribution of the roll directlyafter winding is calculated with a winding model, such as the Hakiel orvon Hertzen winding model. Next, the relaxation of stresses, step IIb,is estimated, by using this result as the initial value, in the timespan before the roll is unwound in the end-use device. In the next stepIII, the stresses obtained from the relaxation model in the precedingstep II are used as initial values, and the strength or runnability 24of the roll during unwinding in the end-use device is estimated. Theestimation can be based, as is the case in this example, on thecalculation model of step IIc. Statistical and empirical results as wellas combinations thereof may also be used. If, based on the estimation,the roll will withstand the process, this selection process of the WOTcurve 26 is complete, step IV. If, based on the estimation, the rollwill not withstand it, there must be a return to step I and a newcandidate for a WOT curve WOT₁(D) 22 has to be selected. Once again,this may be, for example, a constant independent of the diameter, thevalue of the constant being, for instance, 98 percent or 102 percent ofWOT₀(D). If this new WOT curve passes step III, the selection process ofthe WOT curve is complete, step IV. If WOT₁(D) 26 does not satisfy stepIII, iteration has to be continued 25. A new WOT curve candidate can beformed of the two previous ones, by using, for example, a variation ofthe secant method, Erwin Kreyszig: “Advanced Engineering Mathematics”.Sixth Edition, John Wiley & Sons, Inc. 1988, p. 956. This makes itpossible, for instance, to minimize the stress maximum in the RAMAcalculation, step IIc, among other things, in a normed space formed bycontinuous functions. Here, in this description of the procedure, it isassumed that the WOT curve search process produces a curve WOT_(ref)(D)26, which satisfies step III, after steps IIa, IIb and IIc, even thoughit could in principle happen, for example, that the value of WOT wouldat some point exceed the tensile strength of the web, meaning that asuitable solution would not be found.

FIG. 3 shows an example of the search for the initial value 13 of thewinding recipe. In step I, initialization of iteration is carried out 32R_(j)=(N,F,T)_(j)=R₀ (D)=(N₀,F₀,T₀) (D), where (N₀,F₀,T₀) (D) has to berealizable and R_(j)=winding recipe, N=nip loads, F=winding force andT=web tension. The object is to seek the winding recipeR(D)=(N(D),F(D),T(D)) 32 so that, when calculated with the WOT model ofthe wind-up (see Jorkama Dissertation, or empirical model), the windingrecipe gives the WOT curve 12 selected in step I of FIG. 1. Above, N(D)is nip load(s) as a function of the diameter D, F(D) winding force as afunction of the diameter and T(D) web tension before the wind-up as afunction of the diameter. The winding recipe generated as a result ofthis subprocess is marked with R_(ref)(D) 36. In the function form theobjective is thus to find the winding recipe such thatWOT_(ref)(D)=WOT_(model)(R_(ref)(D),D), where the WOT_(model) functionrepresents the WOT model. The procedure is similar to that of otheriterations based on the secant method. First, an initial guess R_(i)=R₀is selected, step I, and a WOT curve WOT_(i)=WOT₀ is calculated, stepII, with a WOT model 33 WOT_(i)=WOT_(model) (R_(i) (D), D). For example,the following values can be used as the initial guess: The nip load aconstant independent of the diameter for as long as possible, thewinding force a constant independent of the diameter, for example, 75percent of web tension and the web tension also a constant independentof the diameter, e.g. 15-20 percent of the tensile strength of the web.If, in the checking of step III 34, WOT₀ is, on the basis of a chosenaccuracy requirement, close enough to WOT_(ref), a transition to step IVcan be made and R₀ can be selected as the winder recipe R_(ref) 36.However, if WOT₀ is not sufficiently accurately WOT_(ref), iteration iscontinued from step II by selecting a new winding recipe R₁ 35. It can,for example, be selected such that the running tension is selected to be98 percent and 102 percent of the running tension of R₀. If this newrecipe 35 passes step III, the winding recipe selection process iscomplete. If R₁ does not realize step III either, iteration has to becontinued. A new winding recipe candidate can be formed out of the twoprevious ones, e.g. using a variation of the secant method. This way,for example, the distance between WOT_(i)(R_(i)(D),D) and WOT_(ref)(D)can be minimized in a normed space formed by continuous vector-valuedfunctions. A metric formed, for example, of the L² norm can be used as adistance function. Limitations due to the mechanics of the wind-up andto the strength of the paper have to be taken into account as aconstraint to minimization.

FIG. 4 presents step V running of slitter-winder 16 of FIG. 1 in moredetail in a case where the slitter-winder comprises WOT measurement. Inshort, recipe R_(ref) 42 is used to run the slitter-winder in thisprocess. However, during the run 43 the recipe is corrected so that themeasured WOT and WOT_(ref) are joined 45. When running theslitter-winder the diameter of the roll being wound up and WOT 44 arecontinuously measured. The WOT measurement can be carried out, forexample, according to the reference Roisum, D., “The Measurement of WebStresses During Roll Winding”, PhD Thesis, Web Handling Research Centerat Oklahoma State University., May 1990. It is checked, at certainintervals (e.g. 5 seconds), whether the measured WOT, marked withWOT_(measurement), is the same or at a set tolerance from WOT_(ref).During the run the winding recipe R_(ref) 46 is continuously changed sothat WOT_(measurement) is the same or at a set tolerance from WOT_(ref).This adjustment can be carried out, for example, as a PID controller, K.Åström & T Hägglund: “PID Controllers: Theory, Design, and Tuning”. 2ndedition, 1995. Pages 59-119. The correction of the recipe is made, forexample, by adjusting primarily winding force, secondarily nip load, andfinally tension. Increasing each winding parameter increases the WOT.

The invention has been described above with reference to one of itsadvantageous exemplifying embodiments only, to the details of which theinvention is by no means intended to be narrowly confined.

For example, the invention is described above with reference to anexample, in which, in the method, the winding recipe of the roll isformed as a function of the diameter. It is also possible to formulatethe winding recipe as a function of the radius or the degree ofthickness of the cumulated paper on the winding core or wound web lengthor the number of laps of the wound web.

1-16. (canceled)
 17. A method of controlling a wind-up in the formationof a roll from a paper web having a strength, comprising the steps of: afirst step of: selecting a WOT (Wound-On-Tension) curve to be controlledto, using a selected starting WOT (Wound-On-Tension) curve, a model ofroll stresses, a model of roll relaxation, and a model of runnability ofa selected end use, by using the selected WOT (Wound-On-Tension) curveas an input to the model of roll stresses which produces an output whichis used in the model of roll relaxation which produces an output formingthe input of the model of runnability of a selected end use, anddetermining if the roll will be damaged in the selected end use, and ifit is determined that the roll will be damaged in the selected end use,using a method for iteration to modify the selected WOT(Wound-On-Tension) curve, and then repeating the first step; a secondstep of: selecting a winding recipe for forming a roll with the selectedWOT (Wound-On-Tension) curve by using a selected starting recipe, and amodel of the wind-up, using the selected starting recipe as an input tothe model of the wind-up, using the output of the model of the wind-upin the model of roll stresses to define a model roll, and determining ifthe model roll formed by the selected starting recipe conforms to theWOT (Wound-On-Tension) curve of the first step within a selectedaccuracy; if the roll formed by the winding recipe does not conform tothe WOT (Wound-On-Tension) curve of the first step within the selectedaccuracy, using a method for iteration to modify the selected startingrecipe and repeat the second step; winding the roll in the wind-up andmeasuring a WOT (Wound-On-Tension) curve; and comparing the measured WOT(Wound-On-Tension) curve as a function of roll diameter, or web length,with the selected WOT (Wound-On-Tension) curve and modifying the windingrecipe so that the measured WOT (Wound-On-Tension) curve is the same asor within a set tolerance of the selected WOT (Wound-On-Tension) curve.18. The method of claim 17 wherein the second step includes constrainingthe winding recipe to limitations due to the mechanics of the wind-upand to the strength of the paper web.
 19. The method of claim 17 whereinthe selected WOT (Wound-On-Tension) curve and the measured WOT(Wound-On-Tension) curve are curves of tension vs a function of rolldiameter, or a function web length.
 20. The method of claim 19 whereinthe function of roll diameter is a function of roll radius or thethickness of cumulated paper on a winding core.
 21. The method of claim19 wherein the function of web length is a function of number of laps ofpaper on a winding core.
 22. The method of claim 17 wherein the methodfor iteration to modify the selected WOT (Wound-On-Tension) curvecomprises a variation of the secant method.
 23. The method of claim 17wherein the selected starting recipe is keeping nip load constantindependent of the diameter for as long as possible, keeping windingforce a constant independent of the diameter, and keeping web tension aconstant independent of the diameter.
 24. The method of claim 17 whereinthe winding recipe is determined as a function of the diameter or radiusor the degree of thickness of the cumulated paper on the winding core oras a function of wound web length or the number of laps of the woundweb.
 25. The method of claim 17 wherein the model of the wind-up is usedto check that the roll will withstand winding in the wind-up.
 26. Amethod of controlling a wind-up in the formation of a roll from a paperweb having a strength, comprising the steps of: a first step of:selecting a WOT (Wound-On-Tension) curve to be controlled to, using aselected starting WOT (Wound-On-Tension) curve, a model of rollstresses, a model of roll relaxation, and a model of runnability of aselected end use, by using the selected WOT (Wound-On-Tension) curve asan input to the model of roll stresses which produces an output which isused in the model of roll relaxation which produces an output formingthe input of the model of runnability of a selected end use, anddetermining if the roll will be damaged in the selected end use, and ifit is determined that the roll will be damaged in the selected end use,using a method for iteration to modify the selected WOT(Wound-On-Tension) curve and then repeating the first step; a secondstep of: selecting a winding recipe for forming a roll with the selectedWOT (Wound-On-Tension) curve by using a selected starting recipe, and amodel of the wind-up, using the selected starting recipe as an input tothe model of the wind-up, using the output of the model of the wind-upin the model of roll stresses to define a model roll, and determining ifthe model roll formed by the selected starting recipe conforms to theWOT (Wound-On-Tension) curve of the first step within a selectedaccuracy; if the roll formed by the winding recipe does not conform tothe WOT (Wound-On-Tension) curve of the first step within the selectedaccuracy, using a method for iteration to modify the selected startingrecipe and repeat the second step; winding the roll in the wind-up; andcontrolling the wind-up, based on the winding recipe.
 27. The method ofclaim 26 wherein during winding the roll in the wind-up, a measured WOT(Wound-On-Tension) curve is monitored to determine whether the selectedWOT curve is realized and, if necessary, the selected winding recipe iscorrected such that a measured WOT (Wound-On-Tension) curve correspondsto the selected WOT (Wound-On-Tension) curve.
 28. The method of claim 26wherein the iteration of the winding recipe is continued in a pluralityof rolls formed in the wind-up.
 29. The method of claim 26 furthercomprising the steps of: indirectly measuring, in three or twodimensions, the internal stress distribution of the roll being wound up;calculating with the model the roll stresses caused by forces directedto the roll during winding; estimating the relaxation of the internalstresses of the roll after finishing before the roll is processed in theselected end use; and calculating with the model of runnability of aselected end use, stresses and displacements directed to the roll duringunwinding.
 30. The method of claim 26 wherein the selected starting WOT(Wound-On-Tension) curve is based on starting data on the paper gradeobtained through off- and on-line measurements of paper processingequipment preceding the wind-up and through measurements made in thewind-up.
 31. The method of claim 30 wherein limitations for the windingrecipe are determined on the basis of basic data obtained throughphysical properties of the winding device and through the model of rollstresses.
 32. The method of claim 26 further comprising the step ofcalculating, in the model of roll stresses, the model of rollrelaxation, and the model of runnability of a selected end use,slippages or other damage mechanisms generated within the roll.